This invention relates to digital signal processing, and has particular relation to one-multiplier Gray-Markel filters used in vehicle navigation systems.
A one-multiplier Gray-Markel filter has one or more stages, each of which includes a multiplier, a delay element, and three summers. The first summer is driven by the filter input and the delay element, the second summer is driven by the filter input and the multiplier, and the third summer is driven by the multiplier and the delay element. The third summer always acts as an adder, but the first summer acts as a subtracter (filter input minus delay element output) when the second summer acts as an adder, and acts as an adder when the second summer acts as a subtracter (filter input minus multiplier output). Each stage therefore has a sign parameter. The sign parameter of a stage is +1 when the second summer acts as an adder, and is -1 when the second summer acts as a subtracter.
The conventional art is embodied in the seminal article, A. H. Gray, Jr. and J. D. Markel, "Digital Lattice and Ladder Filter Synthesis", IEEE Trans. AU, AU-21, pp. 491-500, December, 1973. In that art, the average energy of the signal passing through the filter must be kept below some preselected maximum. That article set out an algorithm for selecting the sign parameter of each stage so that this average energy criterion is met. This criterion is appropriate in, for example, voice synthesis and compression. Overall voice quality is improved when this criterion is selected, even though the filter overflows from time to time. Each overflow is so brief that it is hardly noticeable, and is rapidly damped out by subsequent input signals.
This is not the case in vehicle navigation. Errors do not damp out; they accumulate. This is especially true when the navigation signal is part of a servo loop, used to control the vehicle, and not just locate it. In this case, the maximum signal passing through the filter must be kept below the preselected maximum.